## 016 Radius of the sphere circumscribing a regular triangular pyramid

**Example 016**

Find the area of the surface and the volume of the sphere circumscribed about a regular tetrahedron of edge 25 cm. See Figure 015.

**Example 016**

Find the area of the surface and the volume of the sphere circumscribed about a regular tetrahedron of edge 25 cm. See Figure 015.

**Example 015**

Two balls, one 15 cm in diameter and the other 10 cm in diameter, are placed in a cylindrical jar 20 cm in diameter, as shown in Figure 014. Find the volume of water necessary to cover them.

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**Example 014**

A boy who had discovered that 20 mm marbles fitted snugly into the bottom of a cylindrical jar, dropped in a fourth on top of the three and poured water enough into the jar to just cover them. How much water did he use?

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**Example 013**

Compare the volume of a sphere inscribed in a cube with volume of the sphere that circumscribes the cube.

**Example 012**

Find the volume and total area of the sphere which circumscribes a cylinder of revolution whose altitude and diameter are each 6 inches.

**Example 007**

A spherical balloon is inflated so that so that its diameter is 12 m. Find the surface area of the balloon’s covering and the volume of the gas.

**Example 005**

A cubic foot of ivory weighs 114 lb. Find the weight of 1000 ivory billiard balls 2½ inch in diameter.

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**Example 003**

An iron ball 10 cm in diameter weighs 4 kg. Find the weight of an iron shell 5 cm thick whose external diameter is 50 cm.

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**Problem 002**

Find the weight of the snowball 1.2 m in diameter if the wet compact snow of which this ball is made weighs 480 kg/m^{3}

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**Problem 001**

A 523.6 cm^{3} solid spherical steel ball was melted and remolded into a hollow steel ball so that the hollow diameter is equal to the diameter of the original steel ball. Find the thickness of the hollow steel ball.